Geodesic
Handling ray transform of symmetric tensor fields and the Radon transform of differential forms on incomplete data
Daghestan Electronic Mathematical Reports, Tome 1 (2014), pp. 56-70

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A symmetric tensor field in the Euclidian space of any dimension ${{\mathbb R}}^n$ can be reconstructed from its integrals along straight lines which form n-manifold. We obtained the new formulas reconstructing solenoidal part of the fields when a ray transform is known only on complex lines, intersecting a given curve, as well as a curve belonging to infinity. The new family of two-dimensional planes in ${{\mathbb R}}^n$ is introduced and the inversion formula is obtained for the case of differential forms of degree $2$ on the given integrals along the planes of this family.
Keywords: symmetric tensor field, ray transform, reconstruction, complex of lines, solenoidal part, Radon transform of differential forms. 
@article{DEMR_2014_1_a1,
     author = {Z. G. Medzhidov},
     title = {Handling ray transform of symmetric tensor fields and the {Radon} transform of differential forms on incomplete data},
     journal = {Daghestan Electronic Mathematical Reports},
     pages = {56--70},
     publisher = {mathdoc},
     volume = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DEMR_2014_1_a1/}
}
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Z. G. Medzhidov. Handling ray transform of symmetric tensor fields and the Radon transform of differential forms on incomplete data. Daghestan Electronic Mathematical Reports, Tome 1 (2014), pp. 56-70. http://geodesic.mathdoc.fr/item/DEMR_2014_1_a1/